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Understanding Inverses of Functions in Algebra

Learn about inverse functions, composition of functions, and graphing inverse functions in algebra. Understand how to find the inverse function algebraically and graphically. Verify if two functions are inverses. Get ready for the test with practice problems.

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Understanding Inverses of Functions in Algebra

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  1. September 27, 2012Inverse of Functions Warm-up: f(x) = x2 – 1 and Find the following compositions, then state the domain 1. (f o g)(x) 2. (g o f)(x) CW 1.9: Pg. 99 #15-23odd, Pg. 90 #35, 37 Test Monday/Tuesday!

  2. What are inverses? f-1(x) • Inverse of multiplication is__________________ • Inverse of addition is______________________ • Inverse of a square root is__________________ • Inverse of squared is______________________ • Inverse of the relation {(-5, 4), (-1, 5), (0, 2), (3, 4)} is:

  3. Lesson 1.9Graphs of Inverses – What do you notice?Make a table for each and graph their points. What do you notice about their points? f(x) = 2x – 3 f(x) = x2, x ≥ 0

  4. Finding the Inverse Function, f -1(x), algebraically Find the inverse function of: f(x) = 3x + 2 1) Rewrite f(x) to y 2) Switch the x and y variables. 3) Solve for y

  5. Show that the two functions are inverses algebraically and graphically

  6. The composition of a function and its inverse will always equal x. Let f and g be two functions: Two functions are inverses if and only if: (f o g)(x) = x and (g o f)(x) = x

  7. Verifying that the two functions are inverses: by using the composition, f(f -1(x)) = x f(x) = 3x + 2 Show that the composition of f and f-1 equals x. Replace x in f(x) with (x – 2)/3 YAY! Simplify = x – 2 + 2 f(f -1(x))= x

  8. Now go the other way… f(x) = 3x + 2 f-1(f(x))

  9. Ways to verify two functions are inverses • The compositions of the two functions equal x: (f o g)(x) = x and (g o f)(x) = x • The graph of the inverse function is a reflection of the graph of f over the y = x line. • If the coordinates of the function are (a, b), the inverse function coordinates are (b, a).

  10. Are the following functions two inverses of each other? Show/explain how to check. f(x) = 1 + 7x and

  11. The inverses of function A and D are functions, but B and C are not. Why? Figure out a rule or a test that tells you whether or not it is a function. A B C D

  12. Fill out the chart to help organize our Unit 1 TestUse f(x) = x2 – 9 to find the following

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